Apply the Binomial Theorem to expand the following expression

32 - 80 + 80x³ - 40x² + 10x - 1

Step-by-step explanation:

Using the 5 th row of Pascal's triangle to generate the coefficients

1  5  10  10  5  1

with deceasing powers of 2x from to

and increasing powers of - 1 from to , then

= 1 × + 5 × + 10 × (2x)³(- 1)² + 10 × (2x)²(- 1)³ + 5 × + 1 ×

= 32 - 80 + 80x³ - 40x² + 10x - 1

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